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LU factorization for sparse matrices is an important computing step for many engineering and scientific problems such as circuit simulation. There have been many efforts toward parallelizing and scaling this algorithm, which include the recent efforts targeting the GPUs. However, it is still challenging to deploy a complete sparse LU factorization workflow on a GPU due to high memory requirements and data dependencies. In this paper, we propose the first complete GPU solution for sparse LU factorization. To achieve this goal, we propose an out-of-core implementation of the symbolic execution phase, thus removing the bottleneck due to large intermediate data structures. Next, we propose a dynamic parallelism implementation of Kahn's algorithm for topological sort on the GPUs. Finally, for the numeric factorization phase, we increase the parallelism degree by removing the memory limits for large matrices as compared to the existing implementation approaches. Experimental results show that compared with an implementation modified from GLU 3.0, our out-of-core version achieves speedups of 1.13--32.65X. Further, our out-of-core implementation achieves a speedup of 1.2--2.2 over an optimized unified memory implementation on the GPU. Finally, we show that the optimizations we introduce for numeric factorization turn out to be effective. 

Abstract Electrochemical water oxidation reaction (WOR) to hydrogen peroxide (H 2 O 2 ) via a 2e − pathway provides a sustainable H 2 O 2 synthetic route, but is challenged by the traditional 4e − counterpart of oxygen evolution. Here we report a CO 2 /carbonate mediation approach to steering the WOR pathway from 4e − to 2e − . Using fluorine-doped tin oxide electrode in carbonate solutions, we achieved high H 2 O 2 selectivity of up to 87%, and delivered unprecedented H 2 O 2 partial currents of up to 1.3 A cm −2 , which represents orders of magnitude improvement compared to literature. Molecular dynamics simulations, coupled with electron paramagnetic resonance and isotope labeling experiments, suggested that carbonate mediates the WOR pathway to H 2 O 2 through the formation of carbonate radical and percarbonate intermediates. The high selectivity, industrial-relevant activity, and good durability open up practical opportunities for delocalized H 2 O 2 production. 

Abstract Oxygen reduction reaction towards hydrogen peroxide (H 2 O 2 ) provides a green alternative route for H 2 O 2 production, but it lacks efficient catalysts to achieve high selectivity and activity simultaneously under industrial-relevant production rates. Here we report a boron-doped carbon (B-C) catalyst which can overcome this activity-selectivity dilemma. Compared to the state-of-the-art oxidized carbon catalyst, B-C catalyst presents enhanced activity (saving more than 210 mV overpotential) under industrial-relevant currents (up to 300 mA cm −2 ) while maintaining high H 2 O 2 selectivity (85–90%). Density-functional theory calculations reveal that the boron dopant site is responsible for high H 2 O 2 activity and selectivity due to low thermodynamic and kinetic barriers. Employed in our porous solid electrolyte reactor, the B-C catalyst demonstrates a direct and continuous generation of pure H 2 O 2 solutions with high selectivity (up to 95%) and high H 2 O 2 partial currents (up to ~400 mA cm −2 ), illustrating the catalyst’s great potential for practical applications in the future. 

Electrochemical CO 2 or CO reduction to high-value C 2+ liquid fuels is desirable, but its practical application is challenged by impurities from cogenerated liquid products and solutes in liquid electrolytes, which necessitates cost- and energy-intensive downstream separation processes. By coupling rational designs in a Cu catalyst and porous solid electrolyte (PSE) reactor, here we demonstrate a direct and continuous generation of pure acetic acid solutions via electrochemical CO reduction. With optimized edge-to-surface ratio, the Cu nanocube catalyst presents an unprecedented acetate performance in neutral pH with other liquid products greatly suppressed, delivering a maximal acetate Faradaic efficiency of 43%, partial current of 200 mA⋅cm −2 , ultrahigh relative purity of up to 98 wt%, and excellent stability of over 150 h continuous operation. Density functional theory simulations reveal the role of stepped sites along the cube edge in promoting the acetate pathway. Additionally, a PSE layer, other than a conventional liquid electrolyte, was designed to separate cathode and anode for efficient ion conductions, while not introducing any impurity ions into generated liquid fuels. Pure acetic acid solutions, with concentrations up to 2 wt% (0.33 M), can be continuously produced by employing the acetate-selective Cu catalyst in our PSE reactor. 

The condensation of half-light half-matter exciton polaritons in semiconductor optical cavities is a striking example of macroscopic quantum coherence in a solid-state platform. Quantum coherence is possible only when there are strong interactions between the exciton polaritons provided by their excitonic constituents. Rydberg excitons with high principal value exhibit strong dipole–dipole interactions in cold atoms. However, polaritons with the excitonic constituent that is an excited state, namely Rydberg exciton polaritons (REPs), have not yet been experimentally observed. Here, we observe the formation of REPs in a single crystal CsPbBr 3 perovskite cavity without any external fields. These polaritons exhibit strong nonlinear behavior that leads to a coherent polariton condensate with a prominent blue shift. Furthermore, the REPs in CsPbBr 3 are highly anisotropic and have a large extinction ratio, arising from the perovskite’s orthorhombic crystal structure. Our observation not only sheds light on the importance of many-body physics in coherent polariton systems involving higher-order excited states, but also paves the way for exploring these coherent interactions for solid-state quantum optical information processing.